Corrections to the universal behavior of the Coulomb-blockade peak splitting for quantum dots separated by a finite barrier

Building upon earlier work on the relation between the dimensionless interdot channel conductance g and the fractional Coulomb-blockade peak splitting f for two electrostatically equivalent dots, we calculate the leading small-g correction that results from an interdot tunneling barrier that is not a delta function but, rather, has a finite height V-0 and a nonzero width xi and can be approximated as parabolic near its peak. The finiteness of the barrier leads to a small upward shift of the f-versus-g curve for g much less than 1. The shift is a consequence of the fact that the tunneling matrix elements vary exponentially with the energies of the states connected. For a parabolic barrier, the energy scale for the variation is hw, where w, which is proportional to root V-0/xi, is the harmonic oscillator frequency of the inverted parabolic well. In the limit g-->0, the finite-width f-versus-g curve behaves like (U/hw)/\1ng\, where U is the energy cost associated with moving electrons between the dots.